Abstract
Physical systems with symmetries are described by
functions containing kinematical and dynamical parts. We consider
the case when kinematical symmetries are described by a noncompact
semisimple real Lie group G. Then separation of kinematical
parts in the functions is fulfilled by means of harmonic
analysis related to the group G. This separation depends on
choice of a coordinate system on the space where a physical
system exists. In the paper we review how coordinate systems can
be chosen and how the corresponding harmonic analysis can be done.
In the first part we consider in detail the case when G is the
de Sitter group SO0(1,4). In the second part we show how the
corresponding theory can be developed for any noncompact
semisimple real Lie group.